A kite is flying overhead at an angle of elevation is 28. If the kite string is 10m long, what is the horizontal that the kite is flying away from you?
hypotenuse = 10
10 cos 28 = horizontal leg
To determine the horizontal distance that the kite is flying away from you, you can use trigonometry. In this case, we can use the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle.
In the given scenario, the angle of elevation is 28 degrees, and the length of the kite string (hypotenuse) is 10m. We are trying to find the length of the horizontal side (adjacent).
Using trigonometry, the equation for the tangent function is:
tangent(angle) = opposite / adjacent
In this case, the opposite side is the vertical height, which is not given, but we are interested in the horizontal distance. Therefore, we need to find the length of the adjacent side.
Let's solve for the adjacent side:
tangent(28º) = opposite / adjacent
We can rearrange the equation to solve for the adjacent side:
adjacent = opposite / tangent(28º)
Since the opposite side is not given, we can find it by multiplying the length of the kite string (hypotenuse) by the sine of the angle of elevation:
opposite = 10m * sine(28º)
Now we can substitute the value of the opposite side back into the original equation:
adjacent = [10m * sine(28º)] / tangent(28º)
Using a scientific calculator, you can calculate the value of the tangent and sine for the angle of 28 degrees. After getting those values, you can substitute them into the equation to find the value of the adjacent side, which represents the horizontal distance that the kite is flying away from you.